I have a tester similar to the one shown and that can detect live wires by being near the wire, no contact needed. It will also test fuses or wires for continuity.
I do not think a non-contact meter will detect a fault in a wire if wire still has continuity.
Also no not think much of the YouTube AC Line Detector. Parts may be something like
MPSA13 darlington , 2N3904, couple of resistors, & LED.
I use a high gain audio amp. ( Radio Shack ) with speaker for non contact location of dead Christmas tree lights.
The extremely simple circuit does not detect a damaged insulation part of a high voltage AC wire. It simply detects that a wire has some high voltage AC in it if it is insulated or not.